Question

The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:

• A. 27
• B. 22
• C. 17
• D. 23

Answer 1

The Correct Option is A

Step 1: Problem Definition:
Given a dataset with a mean of 21 and a median of 23, determine the mode.

Step 2: Empirical Relationship:
For moderately skewed distributions, the relationship between mean, median, and mode is empirically defined as:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] This formula is applicable to approximately symmetrical or normally distributed data.

Step 3: Calculation:
Substitute the given values into the formula:
\[ \text{Mode} = 3 \times 23 - 2 \times 21 \] Calculate the result:
\[ \text{Mode} = 69 - 42 = 27 \]

Step 4: Result:
The mode of the dataset is \( 27 \).